Abstract: A work piece of irregular or random outer contours is geometrically determined in its position in a given three-dimensional coordinate system before any supporting and clamping of the work piece. This determination of a precise geometrical work piece position is accomplished with the aid of three and only three flat plane work piece seating surfaces forming part of three spheres having a segment cut off to form the respective flat plane seating surface. The three spheres are held in three spherical sockets which define three pivot points for the respective sphere. The pivot points are fixed in the three-dimensional coordinate system and hence define a first reference plane relative to which the geometrical work piece position is determined. Any subsequent supporting and/or clamping of the position determined work piece does not disturb the position determination.